A likelihood approach to scaling examination marks

Abstract

One of the common approaches
to the problem of scaling and combining
examination marks has its roots in the least squares tradition.
In this framework dealing with examiners' preconceptions about
the transformations has to be done in an {\it ad hoc} way.
Here we investigate a likelihood-based approach, thereby allowing
preconceptions to be handled by standard Bayesian techniques.
It turns out that the
likelihood approach does not directly parallel the least squares one
(essentially because a Jacobian must be included in the likelihood), but
the device of introducing fictitious candidates to deal with prior beliefs
in the least squares set-up can be understood in a Bayesian way.